Renormalization of the Graphene Dispersion Velocity Determined from Scanning Tunneling Spectroscopy

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Renormalization of the Graphene Dispersion Velocity Determined from Scanning Tunneling Spectroscopy

Jungseok Chae, Suyong Jung, Andrea F. Young, Cory R. Dean, Lei Wang, Yuanda Gao, Kenji Watanabe, Takashi Taniguchi, James Hone, Kenneth L. Shepard, Phillip Kim, Nikolai B. Zhitenev, and Joseph A. Stroscio

Phys. Rev. Lett. 109, 116802 – Published 11 September 2012

Abstract

In graphene, as in most metals, electron-electron interactions renormalize the properties of electrons but leave them behaving like noninteracting quasiparticles. Many measurements probe the renormalized properties of electrons right at the Fermi energy. Uniquely for graphene, the accessibility of the electrons at the surface offers the opportunity to use scanned probe techniques to examine the effect of interactions at energies away from the Fermi energy, over a broad range of densities, and on a local scale. Using scanning tunneling spectroscopy, we show that electron interactions leave the graphene energy dispersion linear as a function of excitation energy for energies within $\pm 200 meV$ of the Fermi energy. However, the measured dispersion velocity depends on density and increases strongly as the density approaches zero near the charge neutrality point, revealing a squeezing of the Dirac cone due to interactions.

Received 12 July 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.116802

Authors & Affiliations

Jungseok Chae^1,2, Suyong Jung^1,2,3, Andrea F. Young⁴, Cory R. Dean^5,6, Lei Wang⁶, Yuanda Gao⁶, Kenji Watanabe⁷, Takashi Taniguchi⁷, James Hone⁶, Kenneth L. Shepard⁵, Phillip Kim⁴, Nikolai B. Zhitenev^1,*, and Joseph A. Stroscio^1,†

¹Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
²Maryland NanoCenter, University of Maryland, College Park, Maryland 20472, USA
³Korea Research Institute of Standards and Science, Daejeon, 305-340 Korea
⁴Department of Physics, Columbia University, New York, New York 10027, USA
⁵Department of Electrical Engineering, Columbia University, New York, New York 10027, USA
⁶Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA
⁷National Institute for Materials Science, Tsukuba, Ibaraki 305-0044 Japan

^*nikolai.zhitenev@nist.gov
^†joseph.stroscio@nist.gov

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Vol. 109, Iss. 11 — 14 September 2012

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Images

Figure 1
Local probing of graphene on hBN. (a) STM topographic image of graphene on hBN. The moiré pattern with a unit cell length of 4.5 nm corresponds to a rotation of 3.1° of the graphene lattice relative to the hBN crystal. (b) Differential conductance spectra of graphene on hBN at $V_{G} = - 30 V$ . (c) Spatial variation of the $N = - 1$ LL peak position measured in the same area as (a), reflecting the local disorder potential variation. The positions $A$ and $B$ (white dots) denote electron and hole puddle locations where measurements are reported in Figs. 2, 3, 4.Reuse & Permissions
Figure 2
Gate mapping tunneling spectroscopy of the Landau level density of states of graphene on hBN. Each map is built of individual $d I / d V$ vs $V_{B}$ spectra taken at multiple fixed $V_{G}$ . The color scale is the $d I / d V$ magnitude. (a) $d I / d V$ gate map at $B = 2 T$ obtained in the hole puddle labeled $B$ in Fig. 1c. (b) $d I / d V$ gate map spectra at $B = 5 T$ . The tilted red line indicates an axis of constant density (chemical potential) following the transitions of the LLs as discussed in the text, while the vertical blue line indicates constant $V_{G}$ . The yellow overlays are portions of the simulation in (c). (c) Simulation of the $d I / d V$ gate map spectra at $B = 5 T$ with a constant dispersion velocity of $1.1 \times 10^{6} m / s$ and the probe-sample capacitance determined from the slope of the LL transitions in (b) [24]. Portions of the simulation are overlaid in (b) (yellow lines) showing agreement at high densities and deviations at low densities from using a constant velocity. The white arrow points to the simulated ${LL}_{2}$ position which lies in between the experimental ${LL}_{1}$ and ${LL}_{2}$ peaks at low density.Reuse & Permissions
Figure 3
Landau level dispersion. (a) $d I / d V$ spectra (red line) at constant density obtained along the red line in Fig. 2b. A fit of LL peaks $N = 1$ to $N = 6$ is shown in green using a series of Lorentzians. (Inset) A comparison of the $d I / d V$ spectra at constant gate voltage ( $V_{G} = 12 V$ ) (blue line) and constant density (red line), obtained along the lines indicated in Fig. 2b. The spectra at constant gate voltage overestimates the energy scale by 5% at this density. (b) Determination of the graphene dispersion velocity from the LL peak energy positions (obtained along lines of constant density in the gate maps) for the electron puddle $A$ at $B = 2 T$ . The peak positions are plotted as a function of the square root of the Landau orbital index $N$ and magnetic field $B$ . A linear fit (solid lines) is used to determine the dispersion velocity. (Inset) Residuals from the linear fit showing very good linearity in the LL dispersion.Reuse & Permissions
Figure 4
Renormalized graphene dispersion. (a) Schematic of the Dirac cone variation as a function of density. The data presented in this Letter show that the graphene energy-momentum dispersion remains linear at low energy in the presence of electron interactions, while the Dirac cone angle, which is inversely proportional to the velocity, decreases (gets squeezed) at low density. (b) Renormalized velocity determined from the linear fitting of LL peak positions as described in Fig. 3b as a function of density for the electron (red symbols) and hole (blue symbols) puddle locations $A$ and $B$ at $B = 2 T$ . The solid line shows a fit to the combined data from puddle $A$ and $B$ using Eq. (1) with $v = (0.957 \pm 0.003) \times 10^{6} m / s$ and $r_{s} = (0.69 \pm 0.03)$ [25].Reuse & Permissions

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